P3356 火星探险问题

#include<iostream>
#include<cstdio>
#include<queue>
#include<cstring>
using namespace std;
const int N=5000+10;
const int M=50000+10;
const int INF=0x3f3f3f3f;
int n,m,s,t,bs,k,maxflow,mincost,mp[50][50];
struct edge{
    int nxt,to,cap,cost;
}edges[M<<1];
int cnt=1,head[N],pre[N];

void add_edge(int x,int y,int z,int c) {
    edges[++cnt].nxt=head[x]; edges[cnt].to=y; edges[cnt].cap=z; edges[cnt].cost=c; head[x]=cnt;
}

queue<int> q;
int dis[N],lim[N]; 
bool inq[N];
bool spfa(int s,int t) {
    while (!q.empty()) q.pop();
    memset(dis,0x3f,sizeof(dis));
    memset(inq,0,sizeof(inq));
    dis[s]=0; inq[s]=1; lim[s]=INF; q.push(s);
    while (!q.empty()) {
        int x=q.front(); q.pop();
        for (int i=head[x];i;i=edges[i].nxt) {
            edge e=edges[i];
            if (e.cap && dis[x]+e.cost<dis[e.to]) {
                dis[e.to]=dis[x]+e.cost;
                pre[e.to]=i;  //即e.to这个点是从i这条边来的 
                lim[e.to]=min(lim[x],e.cap);
                if (!inq[e.to]) { q.push(e.to); inq[e.to]=1; }
            }
        }
        inq[x]=0;
    }
    return !(dis[t]==INF); 
}

void MCMF() {
    maxflow=0; mincost=0;
    while (spfa(s,t)) {
        int now=t;
        maxflow+=lim[t];
        mincost+=lim[t]*dis[t];
        while (now!=s) {
            edges[pre[now]].cap-=lim[t];
            edges[pre[now]^1].cap+=lim[t];
            now=edges[pre[now]^1].to;
        }
    }
}

int id(int x,int y) { return (x-1)*m+y; }

void dfs(int k,int x,int y) { //用dfs顺序输出方案 
    if (x==n && y==m) return;
    int u=id(x,y)+bs;
    for (int i=head[u];i;i=edges[i].nxt) {
        int v=edges[i].to;
        if (edges[i].cap<INF) {  //初始流量为INF，小于INF即这条边流过 
            if ((v-1)/m+1>x) printf("%d %d\n",k,0); else printf("%d %d\n",k,1);
            edges[i].cap++;  //重点：是他的流量++，避免下次路径重复 
            dfs(k,(v-1)/m+1,(v-1)%m+1);
            return;
        }
    }
}

//P3356 火星探险问题  费用流+输出路径 
int main()
{
    cin>>k>>m>>n;
    for (int i=1;i<=n;i++) for (int j=1;j<=m;j++) scanf("%d",&mp[i][j]);
    
    s=0; t=2*n*m+1; bs=n*m;
    for (int i=1;i<=n;i++)
        for (int j=1;j<=m;j++) {
            if (mp[i][j]==0) add_edge(id(i,j),id(i,j)+bs,INF,0),add_edge(id(i,j)+bs,id(i,j),0,0);
            if (mp[i][j]==1) add_edge(id(i,j),id(i,j)+bs,0,0),add_edge(id(i,j)+bs,id(i,j),0,0);
            if (mp[i][j]==2) {
                add_edge(id(i,j),id(i,j)+bs,1,-1); add_edge(id(i,j)+bs,id(i,j),0,1);
                add_edge(id(i,j),id(i,j)+bs,INF,0),add_edge(id(i,j)+bs,id(i,j),0,0);
            }
            if (i<n) add_edge(id(i,j)+bs,id(i+1,j),INF,0),add_edge(id(i+1,j),id(i,j)+bs,0,0);
            if (j<m) add_edge(id(i,j)+bs,id(i,j+1),INF,0),add_edge(id(i,j+1),id(i,j)+bs,0,0);
        }
    add_edge(s,id(1,1),k,0); add_edge(id(1,1),s,0,0);
    add_edge(id(n,m),t,k,0); add_edge(t,id(n,m),0,0);
    
    MCMF();
    for (int i=1;i<=maxflow;i++) dfs(i,1,1);  //输出总共有maxflow个方案 
    return 0;
}